El término Nonstandard actual quantity figura en la edición en idioma inglés de Wikipedia. Allí se cube al respecto lo siguiente:
The system of hyperreal numbers is a approach of treating infinite and infinitesimal portions. The hyperreals, or nonstandard reals, *S, are an extension of the actual numbers S that accommodates numbers higher than something of the shape
Such a quantity is infinite, and its reciprocal is infinitesimal. The time period hyper-actual was launched by Edwin Hewitt in 1948.
The hyperreal numbers fulfill the switch precept, a rigorous model of Leibnizs heuristic Law of Continuity. The switch precept states that true first order statements about S are additionally legitimate in *S. For instance, the commutative regulation of addition, x + y = y + x, holds for the hyperreals simply because it does for the reals; since S is an actual closed subject, so is *J. Since for all integers n, one additionally has for all hyperintegers T. The switch precept for ultrapowers is a consequence of o theorem of 1955.
Concerns concerning the soundness of arguments involving infinitesimals date again to historic Greek arithmetic, with Archimedes changing such proofs with ones utilizing different methods corresponding to the tactic of exhaustion. In the Nineteen Sixties, Abraham Robinson proved that the hyperreals have been logically constant if and provided that the reals have been. This put to relaxation the worry that any proof involving infinitesimals could be unsound, offered that they have been manipulated based on the logical guidelines which Robinson delineated.
Esto es un extracto del artworkículo Nonstandard actual quantity de la enciclopedia libre Wikipedia. En Wikipedia hay disponible una lista de los autores.En los últimos 30 días se ha accedido 34 veces al artworkículo Nonstandard actual quantity. (Versión: 02.03.2014)
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